Between 1985 and 1992, The Claim released two albums and various singles and EPs, first on their own record label, and then via Kevin Pearce's Esurient Communications imprint, Bob Stanley's Caff label and the German-based label A Turntable Friend. Their first outing, Armstrong’s Revenge & Eleven Other Short Stories (1985) was followed by the 12" EP This Pencil Was Obviously Sharpened By a Left-Handed Indian Knife Thrower (again on Trick Bag Records). By the time of 1988's Boomy Tella LP, the quality of their politically fused, bittersweet songs had matured considerably, and it is now regarded as their high-water mark. Meanwhile, their single "Wait And See" was recorded at ex-Jam drummer Rick Buckler's studio with ex-Jam producer Vic Coppersmith-Heaven.

The Claim also teamed up with the poet and ex-Dentists drummer Vic Templar (an alias for Ian Smith) for various evenings which combined a play, featuring members of The Claim, with a musical performance by the band. Templar also collaborated with The Claim for the song "Mike The Bike", issued as the B-side to perhaps The Claim's most impressive outing, "Birth Of A Teenager", issued as a limited edition single housed in a sleeve designed by the Medway scene's most multi-faceted talent, Billy Childish. For another gig, Welsh band The Manic Street Preachers played their debut London show supporting The Claim. The Claim played their final show in January 1993.

None of The Claim's music appeared on CD at the time. Recently, the band themselves compiled a retrospective, Black Path, which was released on Rev-Ola Records in September 2009.[2][3] The band played a reunion gig in Rochester, Kent on 19 September 2009 to coincide with the project's release. On Thursday 25 March 2010, they played at a second reunion show with fellow Medway band The Dentists at Dingwalls in Camden Town, London.